php: catch exception and continue execution, is it possible?

Yes but it depends what you want to execute:

E.g.

try {
   a();
   b();
}
catch(Exception $ignored){
}

c();

c() will always be executed. But if a() throws an exception, b() is not executed.

Only put the stuff in to the try block that is depended on each other. E.g. b depends on some result of a it makes no sense to put b after the try-catch block.